Concept explainers
Normalize the following wavefunctions over the range indicated. You may have to use the integral table in Appendix 1.
(a)
(c)
(e)
Trending nowThis is a popular solution!
Chapter 10 Solutions
Physical Chemistry
- One of the most famous of the obsolete theories of the hydrogen atom was proposed by Bohr. It has been replaced by quantum mechanics but, by a remarkable coincidence (not the only one where the Coulomb potential is concerned), the energies it predicts agree exactly with those obtained from the Schrödinger equation. In the Bohr atom, an electron travels in a circle around the nucleus. The Coulombic force of attraction (Ze2/4πε0r2) is balanced by the centrifugal effect of the orbital motion. Bohr proposed that the angular momentum is limited to integral values of ħ. When the two forces are balanced, the atom remains in a stationary state until it makes a spectral transition. Calculate the energies of a hydrogenic atom using the Bohr model.arrow_forwardWhat is the ionization energy (J) of an electron from the n=8 stationary in the hydrogen atom (answer in 3 sig figs)arrow_forwardWhich of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?arrow_forward
- Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10-5 m)3. Suppose that T = 0.9Tc. How many atoms are in the ground state? How close is the chemical potential to the ground-state energy? How many atoms are in each of the (threefold-degenerate) first excited states?arrow_forwardFor the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L (between x = 0 and x = L). Show that the wavefunctions with n = 1 and 2 are orthogonal; you will find the necessary integrals in the Resource section) ,show that the wavefunctions with n = 2 and 4 are orthogonal.arrow_forwardConsider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).arrow_forward
- The electronic spectrum of the molecule butadiene, H2C=CH–CH=CH2, can be approximated using the one-dimensional particle-in-a-box if one assumes that the conjugated double bonds span the entire four-carbon chain. If the electron absorbing a photon having wavelength 217 nm is going from the level n =2 to the level n =3, what is the approximate length of the C4H6 molecule?arrow_forwardWhat is the significance of the y-intercept of a Rydberg plot?arrow_forwardIf n = 4, what can be values for I.what information we can get from this values?arrow_forward
- It takes 155./kJmol to break a fluorine-fluorine single bond. Calculate the maximum wavelength of light for which a fluorine-fluorine single bond could be broken by absorbing a single photon. Round your answer to 3 significant digits.arrow_forwardWhat is the energy of a single photon of microwave radiation with a wavelength of 0.0618 meters? Your answer should have 3 sig figs.arrow_forwardA particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized wavefunction ψ(x) = a1/2e–ax/2, where a is a constant. Evaluate the expectation value of the position operator.arrow_forward
- Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningIntroductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning